How do I add more polygons?
When you create your primitive object you always have the possibility to change some parameters on the bottom of the Tools panel, if you increase Segments and Rings it will create more polygons. If you ever move your object or go in Edit mode, though, you won't have access to these parameters anymore.

But actually when you sculpt there's a tool called Dyntopo that allows you to increase the topology only on the area you sculpt with your brush, that is useful because you don't need to increase your object up to a crazy amount of polygons if you don't need details everywhere. The lower the dyntopo Detail Size factor is the more it will add polygons.

Anyway, even if you end up with a very high poly at the end you can come back to a lower poly with tricks like baking the normals for a low poly version of your object (in this case, before any Dyntopo, save the low-poly version).

You could also dig into the Multiresolution modifier, nice way to sculpt.